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4 years ago

5(x+y)-3(y/x) plz help me

Mathematics

1 answer:

Contact [7]4 years ago

4 0

Answer:

$\large\boxed{5(x+y)-3\left(\dfrac{y}{x}\right)=5x+5y-\dfrac{3y}{x}}$

Step-by-step explanation:

$5(x+y)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=5x+5x\\\\3\left(\dfrac{y}{x}\right)=\dfrac{3y}{x}\\\\5(x+y)-3\left(\dfrac{y}{x}\right)=5x+5y-\dfrac{3y}{x}$

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Find the equation of the line tangent to the graph of

garik1379 [7]

Answer:

$\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}$

Step-by-step explanation:

We want to find the equation of the line tangent to the graph of:

$\displaystyle y=\sin^{-1}\big(\frac{x}{5}\big)\text{ at } x=\frac{5}{2}$

So, we will find the derivative of our equation first. Applying the chain rule, we acquire that:

$\displaystyle y^\prime=\frac{1}{\sqrt{1-(\frac{x}{5})^2}}\cdot\frac{1}{5}$

Simplify:

$\displaystyle y^\prime=\frac{1}{5\sqrt{1-\frac{x^2}{25}}}$

We can factor out the denominator within the square root:

$\displaystyle y^\prime =\frac{1}{5\sqrt{\frac{1}{25}\big(25-x^2)}}$

Simplify:

$\displaystyle y^\prime=\frac{1}{\sqrt{25-x^2}}$

So, we can find the slope of the tangent line at <em>x</em> = 5/2. By substitution:

$\displaystyle y^\prime=\frac{1}{\sqrt{25-(5/2)^2}}$

Evaluate:

$\displaystyle y^\prime=\frac{1}{\sqrt{75/4}}=\frac{1}{\frac{5\sqrt{3}}{2}}=\frac{2\sqrt{3}}{15}$

We will also need the point at <em>x</em> = 5/2. Using our original equation, we acquire that:

$\displaystyle y=\sin^{-1}(\frac{1}{2})=\frac{\pi}{6}$

So, a point is (5/2, π/6).

Finally, by using the point-slope form, we can write:

$\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}(x-\frac{5}{2})$

Distribute:

$\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}x+\frac{-\sqrt{3}}{3}$

Isolate. Hence, our equation is:

$\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}$

7 0

3 years ago

Simplify: (4 /5 + 6/ 25 ) X (8/ 9 + −8 /7 )

Westkost [7]

Answer: -416/1575

Step-by-step explanation:

$\frac{4}{5}=\frac{20}{25} \implies \frac{4}{5}+\frac{6}{25}=\frac{26}{25}\\$

$\frac{8}{9}=\frac{56}{63}\\\\-\frac{8}{7}=-\frac{72}{63}\\\\\implies \frac{8}{9}-\frac{8}{7}=-\frac{16}{63}$

$\frac{26}{25} \times -\frac{16}{63}=-\frac{416}{1575}$

6 0

2 years ago

382.993 to the nearest hundred hundred

MakcuM [25]

Answer:

400

Step-by-step explanation:

382.993 is lies between 300 and 400

and 400 is nearest hundred of 382.993

5 0

3 years ago

Read 2 more answers

Does anyone understand how to solve this?

Nataliya [291]

a f(a) is the function f(x) where x is replaced by a.

So we have

(3x^2 + x + 3 - (3a^2 + a + 3)) / ( x - a)

= (3x^2 - 3a^2 + x - a) / (x = a) Answer

b (3(x + h)^2 + x + h + 3 - (3x^2 + x + 3)) / h

= (3x^2 + 6xh + 3h^2 + x + h - 3x^2 - x - 3) ) / h

= (6xh + h + 3 h^2) / h

= 6x + 3h + 1 Answer

6 0

3 years ago

Please help me:) !!!!!!

Naily [24]

Answer:

Please find the solution in the image attached below.

Step-by-step explanation:

Tcos60 -2T sin(90-theta) = 0

Tcos60 = 2T(cos theta)

cos 60 = 2cos theta

cos60 = 2cos theta

1/4 = cos theta

theta = 75.5

So the angle to the vertical = 90-75.5 = 14.5

Resolving perpendicular

Tsin60 + 2Tsin75.5 - 2g = 0

T(sin 60 + 2sin75.5) = 2g

T = 19.6/sin 60 + 2sin75.5

T = 19.6/1.936 + 0.866

T = 19.6/2.802 = 7.0N

Hope this helps!

6 0

3 years ago